When light interacts with matter, for example via transmission or reflection, it carries away information about the physical and chemical properties of the matter with which it interacted. A property of the light, for example its intensity, may be measured and interpreted to provide information about the matter with which it interacted. That is, the data carried by the light through its intensity may be measured to derive information about the matter.
In general, it is difficult to convert a simple measurement of light intensity into information because of interfering data. That is, several factors may contribute to the intensity of light, even in a relatively restricted wavelength range. It is often impossible to adequately measure the data relating to one of these factors, because the contribution of the other factors is unknown.
It is possible, however, to derive information from light. An estimate may be obtained, for example, by separating light from several samples into wavelength bands, performing a multiple linear regression of the intensity of these bands, and comparing these against the results of conventional measurements of the desired information for each sample. Light from each of several samples may be directed to a series of bandpass filters which separate predetermined wavelength bands from the light. Light detectors following the bandpass filters measure the intensity of each light band. Using conventional means, a multiple linear regression of several measured bandpass intensities may produce an equation such as:y=a0+a1w1+a2w2+ . . . +anwn  (Equation 1)where y is an estimated parameter, an is a constant determined by the regression analysis, and wn is the light intensity for each wavelength band.
Depending on the circumstances, however, the estimate may be unacceptably inaccurate, because other factors may affect the intensity of the wavelength bands. Moreover, these other factors may change from one sample to the next in an inconsistent manner.
A more accurate estimate may be obtained by compressing the data carried by the light into principal components. To obtain the principal components, spectroscopic data is collected for a variety of samples of the same type of light. The light samples are spread into their wavelength spectra by a spectrograph so that the magnitude of each light sample at each wavelength may be measured. This data is then pooled and subjected to a linear-algebraic process known as singular value decomposition (SVD). SVD is at the heart of principal component analysis, which is generally well known by routineers in this art apart from the particular teachings of the present disclosure.
Briefly, principal component analysis is a dimension reduction technique which takes m spectra with n independent variables and constructs a new set of eigenvectors that are linear combinations of the original variables. The eigenvectors may be considered a new set of plotting axes. The primary axis, termed the first principal component, is the vector which describes most of the data variability. Subsequent principal components describe successively less sample variability, until only noise is described by the higher order principal components.
Typically, the principal components are determined as normalized vectors. Thus, each component of a light sample may be expressed as xn {circumflex over (z)}n, where xn is a scalar multiplier and {circumflex over (z)}n is the normalized component vector for the nth component. That is, {circumflex over (z)}n is a vector in a multi-dimensional space where each wavelength is a dimension. Normalization determines values for a component at each wavelength so that the component maintains its shape and so that the length of the principal component vector is equal to one. Thus, each normalized component vector has a shape and a magnitude so that the components may be used as the basic building blocks of all light samples having those principal components. Accordingly, each light sample may be described in the following format by the combination of the normalized principal components multiplied by the appropriate scalar multipliers:x1{circumflex over (z)}1+x2{circumflex over (z)}2+ . . . +xn{circumflex over (z)}n  (Equation 2)The scalar multipliers xn may be considered the “magnitudes” of the principal components in a given light sample when the principal components have a standardized magnitude as provided by normalization.
Because the principal components are orthogonal, they may be used in a relatively straightforward mathematical procedure to decompose a light sample into the component magnitudes which accurately describe the data in the original sample. Since the original light sample may also be considered a vector in the multi-dimensional wavelength space, the dot product of the original signal vector with a principal component vector is the magnitude of the original signal in the direction of the normalized component vector. That is, it is the magnitude of the normalized principal component present in the original signal. This is analogous to breaking a vector in a three dimensional Cartesian space into its X, Y and Z components. The dot product of the three-dimensional vector with each axis vector, assuming each axis vector has a unity magnitude, gives the magnitude of the three dimensional vector in each of the three directions. The dot product of the original signal and some other vector that is not perpendicular to the other three dimensions provides redundant data, since this magnitude is already contributed by two or more of the orthogonal axes.
Because the principal components are orthogonal, or perpendicular, to each other, the dot, or direct, product of any principal component with any other principal component is zero. Physically, this means that the components do not interfere with each other. If data is altered to change the magnitude of one component in the original light signal, the other components remain unchanged. In the analogous Cartesian example, reduction of the X component of the three dimensional vector does not affect the magnitudes of the Y and Z components.
Principal component analysis provides the fewest orthogonal components that can accurately describe the data carried by the light samples. Thus, in a mathematical sense, the principal components are components of the original light that do not interfere with each other and that represent the most compact description of the entire data carried by the light. Physically, each principal component is a light signal that forms a part of the original light signal. Each has a shape over some wavelength range within the original wavelength range. Summing the principal components produces the original signal, provided each component has the proper magnitude.
The principal components comprise a compression of the data carried by the total light signal. In a physical sense, the shape and wavelength range of the principal components describe what data is in the total light signal while the magnitude of each component describes how much of that data is there. If several light samples contain the same types of data, but in differing amounts, then a single set of principal components may be used to exactly describe (except for noise) each light sample by applying appropriate magnitudes to the components.
Thus, the principal components of light may be used to accurately estimate information carried by the light. Accordingly, light that has interacted with a test sample of a known material contaminated with an unknown quantity of a known contaminant can be resolved into its principal components and compared to previously-measured principal components of reference samples with known quantities of contaminants to determine the quantity of contaminant within the test sample.
Most optical sensors include a source of light, or electromagnetic radiation, that interacts with a subject and then shines upon a detector, or radiation transducer. However, despite the mathematical sophistication of today's optical sensors to extract useful information from light, if there is misalignment between the light source and the detector, a portion of the emitted beam may not be optimally measured by the detector, and the sensor output will lose sensitivity and/or accuracy.
As used herein, the term “electromagnetic radiation” refers to radio waves, microwave radiation, infrared and near-infrared radiation, visible light, ultraviolet light, X-ray radiation and gamma ray radiation.
As used herein, the term “detector” may be any device capable of detecting electromagnetic radiation, and may be generally characterized as an optical transducer. For example, the detector may be, but is not limited to, a thermal detector such as a thermopile or photoacoustic detector, a semiconductor detector, a piezo-electric detector, charge coupled device detector, video or array detector, split detector, photon detector (such as a photomultiplier tube), photodiodes, local or distributed optical fibers, and/or combinations thereof, or the like, or other detectors known to those ordinarily skilled in the art. The detector is further configured to produce an output signal, usually in the form of a voltage or current.
Alignment of optical components by machining parts does not account for variation in assembly or in the manufacturing of subassemblies or individual parts. For example, many lamps are known to have a high degree of variation in the filament-to-reflector distance, which creates deviations in proper component alignment.
Accordingly, it is desirable to provide a method and system for quickly and precisely aligning components of optical sensors.